La conjecture locale de Gan-Gross-Prasad pour les groupes unitaires
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Auteur / Autrice : | Raphaël Beuzart-Plessis |
Direction : | Jean-Loup Waldspurger |
Type : | Thèse de doctorat |
Discipline(s) : | Mathématiques |
Date : | Soutenance en 2013 |
Etablissement(s) : | Paris 6 |
Mots clés
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Mots clés contrôlés
Résumé
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EN
In this thesis we consider the local Gan-Gross-Prasad conjecture for unitary groups over a p-adic field. This conjecture predicts a close link between branching laws for a pair (U(n-1),U(n)) of unitary groups and certain epsilon factors. This prediction is based upon the hypothetical local Langlands correspondance for unitary groups. Assuming this correspondance, the main result of this thesis is a proof of the Gan-Gross-Prasad conjecture for tempered representations (part III). In parts I and II, two parallel integral formulas are established: one for a multiplicity and the other one for certain epsilon factors of pairs. Using the theory of endoscopy, we are then able to connect the two formulas and to deduce from them the conjecture.